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Puzzling observations of both thermal and dielectric responses inmulti-silicate glasses at low temperatures $T$ to static magnetic fields $B$have been reported in the last decade and call for an extension of the standardtwo-level systems tunneling model. An explanation is proposed, capable ofcapturing at the same time the $T$- and $B$-dependence of the specific heat$C_p$ and of the dielectric constant $\epsilon$ in these glasses. This theorypoints to the existence of anomalous multi-welled tunneling systems in theglasses -- alongside the standard two-level systems -- and indications aregiven for glasses which should achieve larger electric magnetocapacitiveenhancements.

Multi-Welled Tunneling Model for the Magnetic-Field Effect in Ultracold Glasses